Our weak scaling assumption is a significantly weaker version of the scaling hypothesis of Kolmogorov's 1941 theory and allows for intermittent corrections. Our main technical tool is a statisical version of the well-known Kármán–Howarth–Monin relation [1]}, [2]}, [3]}, that relates the evolution of 2-point correlations to the longitudinal structure function \(S_{\Vert }^3\) , which is, roughly speaking, defined as
\(S_{\Vert }^3(|\ell |)\Bigl \langle \Bigl ((u(x+\ell )-u(x))\cdot \widehat{\ell }\Bigr )^3\Bigr \rangle ,\quad \widehat{\ell }\frac{\ell }{|\ell |}.\) 
